Given a unity feedback system with open loop transfer function, $$$G\left(s\right)=\frac K{s\left(s+1\right)\left(s+2\right)}$$$ The root locus plot of the system is of the form.

Block diagram model of a position control system is shown in figure.
(a) In absence of derivative feedback (K_t=0) , determine damping ratio of the system for amplifier gain K_A=5. Also find the steady state error to unit ramp input.

(b) Find suitable values of the parameters K_A and K_t so that damping ratio of the system is increased to 0.7 without affecting the steady state error as obtained in part (a).

Bode plot of a stable system is shown in fig. The transfer function of the system is

A process with open-loop model $$G(s) = {{K{e^{ - s{\tau _d}}}} \over {\tau s + 1}},$$ is controlled by a PID controller. For this process